Ejercicios derivadas 2

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Derivadas
_____
1 (axn)' = n·axn­1
(3x2)' = 6x1
(3x9)' = 27x8
(11x3)' = 33x2
(5x9)' = 45x8
2 TRIGONOMÉTRICAS
(sen(x))' = cos(x)
(cos(x))' = ­sen(x)
( sen(f(x)) )' = cos(f(x))·f'(x)
( cos(f(x)) )' = ­sen(f(x))·f'(x)
( sen(6x6) )' = Cos(6x6)·( 36x5 )
( Cos(6x19) )' = ­sen(6x19)·( 114x18 )
( sen(8x21) )' = Cos(8x21)·( 168x20 )
( Cos(­3x19) )' = ­sen(­3x19)·( ­57x18 )
( sen(4x2) )' = Cos(4x2)·( 8x1 )
( Cos(2x7) )' = ­sen(2x7)·( 14x6 )
( sen(11x16) )' = Cos(11x16)·( 176x15 )
( Cos(­2x17) )' = ­sen(­2x17)·( ­34x16 )
3 (f(x)n)' = nf(x)n­1·f'(x)
(sen9(x))' = 9·sen8(x)·cos(x)
(cos14(x))' = ­14·cos13(x)·sen(x)
(sen15(x))' = 15·sen14(x)·cos(x)
(cos14(x))' = ­14·cos13(x)·sen(x)
(sen4(x))' = 4·sen3(x)·cos(x)
(cos9(x))' = ­9·cos8(x)·sen(x)
(sen10(x))' = 10·sen9(x)·cos(x)
(cos3(x))' = ­3·cos2(x)·sen(x)
(sen4(x))' = 4·sen3(x)·cos(x)
(cos18(x))' = ­18·cos17(x)·sen(x)
4 (f·g)'=f '·g + f·g'
(18x19·sen(x))' = 342x18·sen(x) + 18x19·cos(x)
(3x11·cos(x))' = 33x10·cos(x) ­ 3x11·sen(x)
(8·sen(x))' = 0·sen(x) + 8cos(x) = 8cos(x)
(16·cos(x))' = 0·cos(x) ­ 16sen(x) = 16sen(x)
5 (fog)'(x)=(f(g(x))' = f'(g(x))·g'(x)
(sen(5x6))' = (cos(5x6)) · 30x5
(6sen(1x15))' = 6cos(1x15) · 15x14
6 (f/g)' = (f '·g­fg')/g2
(tan(x))' = (sen(x)/cos(x))' = (cos(x)·cos(x)­sen(x)·(­sen(x))

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)/cos2(x) = 1/cos2(x)
( (17x+13)/(7x+16))' = ( (17·(7x+16) ­ (17x+13)·7 ) / (7x+16)2
( (8x+2)/(8x+8))' = ( (8·(8x+8) ­ (8x+2)·8 ) / (8x+8)2
( (15x+14)/(18x+15))' = ( (15·(18x+15) ­ (15x+14)·18 ) / (18x+15)2
( (6x+2)/sen(x) )' = ( (6·sen(x) ­ (6x+2)·cos(x) ) / sen2(x)
( (8x+7)/cos(x) )' = ( (8·cos(x) + (8x+7)·sen(x) ) / cos2(x)
7 EXPONENCIALES
(ex)'=ex
(ef(x))'=ef(x)·f'(x)
(e10x8
)' = (e10x8
)·(80x7)
(e8x10
)' = (e8x10
)·(80x9)
(e10x7
)' = (e10x7
)·(70x6)
(e4x3
)' = (e4x3
)·(12x2)
(e12x7
)' = (e12x7
)·(84x6)
(esen(x))' = (esen(x))·cos(x)
(esen(8x))' = (esen(8x))·cos(8x)·8
(esen(1x2))' = (esen(1x2))·cos(1x2)·2x
(1f(x))' = (1f(x))·f'(x)·ln(1)
(16x+11))' = (16x+11))·6·ln(1)
(87x5
)' = (87x5
)·(35x4)·ln(8)
(43x+8))' = (43x+8))·3·ln(4)
(43x9
)' = (43x9
)·(27x8)·ln(4)
(611x+10))' = (611x+10))·11·ln(6)
(611x7
)' = (611x7
)·(77x6)·ln(6)
(34x+4))' = (34x+4))·4·ln(3)
(124x5
)' = (124x5
)·(20x4)·ln(12)
(44x+5))' = (44x+5))·4·ln(4)
(114x4
)' = (114x4
)·(16x3)·ln(11)
(83x+4))' = (83x+4))·3·ln(8)
(113x11
)' = (113x11
)·(33x10)·ln(11)
(89x+5))' = (89x+5))·9·ln(8)
8 LOGARÍTMICAS
(ln(x))'=1/x
(ln(f(x)))'= f'(x) / f(x)
(loga(f(x)))'= f'(x) / f(x) · loga(e)
(ln(14x11))' = ( 154x10 ) / ( 14x11 )
(log11(15x5))' = ( 75x4 ) / ( 15x5 ) · log11(e)
(ln(3x1))' = ( 3x0 ) / ( 3x1 )
(log11(6x2))' = ( 12x1 ) / ( 6x2 ) · log11(e)
(ln(12x8))' = ( 96x7 ) / ( 12x8 )
(log2(18x7))' = ( 126x6 ) / ( 18x7 ) · log2(e)
(ln(13x4))' = ( 52x3 ) / ( 13x4 )
(log11(12x10))' = ( 120x9 ) / ( 12x10 ) · log11(e)
(ln(11x5))' = ( 55x4 ) / ( 11x5 )
(log3(11x6))' = ( 66x5 ) / ( 11x6 ) · log3(e)
y' = ( x12x+13 )'=
y' = y · ( (12x+13)·ln(x) )' = y · ( 12·ln(x) + (12x+13)·1/x ) =

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x12x+13 · ( 12·ln(x) + (12x+13)·1/x )
La expresión se puede simplificar:
y' = x12x+12·( 12·ln(x) + (12x+13) )/x
y' = ( x17x+15 )'=
y' = y · ( (17x+15)·ln(x) )' = y · ( 17·ln(x) + (17x+15)·1/x ) =
x17x+15 · ( 17·ln(x) + (17x+15)·1/x )
La expresión se puede simplificar:
y' = x17x+14·( 17·ln(x) + (17x+15) )/x
y' = ( x13x+3 )'=
y' = y · ( (13x+3)·ln(x) )' = y · ( 13·ln(x) + (13x+3)·1/x ) = x13x+3 ·
( 13·ln(x) + (13x+3)·1/x )
La expresión se puede simplificar:
y' = x13x+2·( 13·ln(x) + (13x+3) )/x
y' = ( x17x+6 )'=
y' = y · ( (17x+6)·ln(x) )' = y · ( 17·ln(x) + (17x+6)·1/x ) = x17x+6 ·
( 17·ln(x) + (17x+6)·1/x )
La expresión se puede simplificar:
y' = x17x+5·( 17·ln(x) + (17x+6) )/x
y' = ( x4x+9 )'=
y' = y · ( (4x+9)·ln(x) )' = y · ( 4·ln(x) + (4x+9)·1/x ) = x4x+9 · (
4·ln(x) + (4x+9)·1/x )
La expresión se puede simplificar:
y' = x4x+8·( 4·ln(x) + (4x+9) )/x
y' = ( x14x+10 )'=
y' = y · ( (14x+10)·ln(x) )' = y · ( 14·ln(x) + (14x+10)·1/x ) =
x14x+10 · ( 14·ln(x) + (14x+10)·1/x )
La expresión se puede simplificar:
y' = x14x+9·( 14·ln(x) + (14x+10) )/x